Radioactivity. Physics 102 Workshop #12. General Instructions

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1 Radioactivity Physics 102 Workshop #12 Name: Lab Partner(s): Instructor: Time of Workshop: General Instructions Workshop exercises are to be carried out in groups of three. One report per group is due by the end of the class. Each week s workshop session would typically contain three sections. The first two sections must be completed in class. The third section should be attempted if there is time. 1. A pre-lab reading and assignment section 2. Experiment section 3. Practice questions and problems PART I: Review As you know, atoms consist of a nucleus at its center, plus electrons bound to it. The nucleus holds the positive charge of the atom. This charge results from the fact that protons are one of its two inhabitants. Each proton is positively charged. Its charge-magnitude is equal to that of the electron. The nucleus has a second inhabitant, called the neutron. The neutron has zero electric charge. Most atoms in nature are neutral. In a neutral atom, the number of electrons bound to the nucleus is equal to the number of protons within the nucleus. As an example, consider hydrogen. By definition, all hydrogen atoms contain one proton in its nucleus. The most prevalent form of hydrogen contains zero neutrons in its nucleus. This is ordinary hydrogen. Its symbol is 1 H1. The subscript is the number of protons in the nucleus (atomic number). The superscript is the sum total of protons and neutrons (mass number). If a hydrogen nucleus contains 1 neutron, we call the nucleus deuterium. Hence, its symbol is 2 H1, as there are two particles in the nucleus. If the nucleus contains two neutrons, it is called tritium. The symbol, then, is 3 H1. The term isotope denotes nuclei that contain the same number of protons, but differing numbers of neutrons. Thus, ordinary hydrogen, deuterium, and tritium are all isotopes of hydrogen, as the nuclei of all three contain just one proton. Consider again the three isotopes of hydrogen ordinary, deuterium and tritium. It happens that the tritium nucleus is unstable. It decays (breaks up) spontaneously. It decays into 3 He2. In the process of this change, an electron is released. The electron is one example of what is called a beta particle. 1

2 Whenever a nucleus spontaneously emits a particle, the nucleus is termed radioactive. Hence, tritium is an example of a radioactive nucleus. Another element with radioactive isotopes is potassium (symbol K). About 93% of the potassium on earth is of the isotope 39 K19. This means there are 19 protons (this defines potassium) and that the sum of the number of protons and neutrons is 39. This prevalent isotope is not radioactive. But 0.012% of all potassium on the earth is the isotope 40 K19. This isotope is radioactive. Note that it has one more neutron (twenty one) than does 39 K19. When 40 K19 undergoes radioactive decay, a high-energy beta particle (electron) is emitted from its nucleus. One of its neutrons is transformed into a proton. What is the resulting nucleus? Since there are now 20 protons, the nucleus is now represented by the symbol 40 Ca20. Note that calcium (symbol Ca) is defined by the fact that there are 20 protons in its nucleus. Note: the superscript does not change - a neutron is transformed into a proton, leaving their sum unchanged. Also, 40 Ca20 is stable. Every second of the day, your body is bombarded by high energy radiation. Its origin is from the sun, or from other celestial objects. This radiation is called background radiation. Today, you will investigate this radiation. You will then investigate some properties of radioactive 40 K19. PART II: The experiment Purpose To learn methods for detecting and counting background radiation and also detecting particles emitted by deliberately-placed radioactive sources. To learn properties of radioactivity. Equipment Potassium Chloride Geiger tubes and counters Ruler Set of barriers: Paper Cardboard Aluminum foil Aluminum slab Lead slab Part A: Geiger counter setup Familiarize yourself with the Geiger counter. It is a device that is sensitive to high energy particles. If a high energy particle enters the counter, it produces ions in the gas that fill the tube. These ions then produce an electrical pulse. The electrical pulse then produces an audio pulse, and also registers a count on the counter. 2

3 Plug in the counter. Make sure that the switch on the back is set to 900 (V), and that the audio is in the ON position. Set the count mode to Continuous. Turn on the Geiger counter. You should hear beeps. Each beep corresponds to the passage of a high energy particle passing through the tube. If you do not hear beeps, bring it to the attention of your instructor. Part B: Quantitative Determination of the Background Radiation 1. Here, we will measure the background radiation around us. Use your watch to measure the number of counts which the Geiger counter records in a 60 second time interval. To do this, first, hold the RESET button. When you are ready to begin timing, let go of the RESET button. After 60 seconds, record the number of counts in Table 1 below. Repeat this 5 times. TRIAL Average Table 1 NUMBER OF COUNTS 2. Using the data from 1, compute the average background radiation rate in counts per minute. You can use: Rate (counts per minute) = Number of counts / time interval (in minutes). Part C. Effect of the Tube-to-Source Distance on the Count Rate Now examine the Geiger counter and its holder. You will notice that the plastic holder has six slots notched in its sides. These notches support a shelf which slides in and out. The upper-most shelf is in position 1, and the bottom-most slot is in position Measure the distance from the opening to the tube, to the middle of each slot. Fill in your measurement-results in Table 2 below. 2. Get about 1 teaspoon of potassium chloride (KCl) and place it on the shelf of position 1. Measure the number of counts which occur in 120 seconds. Then, repeat, for positions 2, 4, and 6. Don t forget to RESET after each measurement. Record your data in Table The uncertainty in the number of counts can be shown, for radioactive decay, to be approximately equal to the square-root of the number of counts. Compute the uncertainties and fill in their values in the table. 4. The count-rate is obtained as before. Simply divide the number of counts by the time-interval. To get the count-rate uncertainty, divide the count uncertainty by the time interval. Fill in these last two columns of Table Make a graph of the count-rate versus distance d in the chart provided. 3

4 6. Draw circles to represent the points on this graph. 7. Draw vertical lines through the center of the points, to indicate the uncertainty in your measurement. SHELF POSITION DISTANCE (CM) NUMBER OF COUNTS UNCERAINTY IN NUMBER OF COUNTS COUNT-RATE (COUNTS PER MINUTE) UNCERTAINTY (COUNTS PER MINUTE) Table 2 The Graph of Count-Rate versus distance from radioactive source to the Geiger Tube 4

5 Part D: Computing the KCl Count-Rate The data you have collected (when KCl was on a shelf) includes more than the radiation from KCl. It also includes radiation from the background. To get the rate from just KCl, it is necessary to subtract out the background rate. Refer to your results from Part B, for the background rate. Note the average value of your results for this entry. Then compute and record the background-subtracted count-rate (for KCl alone). Note: The uncertainty-rate is the same as you found in Table 2. SHELF POSITION DISTANCE (CM) COUNT- RATE (COUNTS PER MINUTE) BACKGROUND RATE COUNT-RATE FOR KCL ALONE (COUNTS PER MINUTE) UNCERTAINTY (COUNTS PER MINUTE) Table 3: Background Subtraction of the KCl Count-rates 5

6 Make a graph of the count-rate versus distance d in the chart provided. Do you observe that the KCl count-rate increases, decreases, or remains the same as d increases? If you found that the count-rate changes as d changes, is the change linear or non-linear? Note: When we say that a change is linear, it means the following: You make a change in one variable. Call it x. Then, you observe the change resulting in the other variable. Call this change y. You then repeat the process, using the same x, but starting at some other value of x. If you get the same value for y as before, then the dependence is linear. This must be true, no matter what value of x you start with. 6

7 Part E: Effects of Barriers on the Counting Rate You will now determine whether the beta particles (usually written as β particles) emitted by KCl can penetrate various materials. The materials used as barriers will be paper, cardboard, aluminum foil, a thin aluminum slab, and a lead slab. Place the KCl salt in Position 2. Measure the number of counts in a two-minute interval. Fill in your result in the row labeled None in Table 3 below. Repeat the experiment with various barriers placed into Position 1 so as to block the path of the β particles. Fill in your results in table 3. BARRIER NUMBER OF COUNTS COUNT RATE None Paper Cardboard Aluminum foil Aluminum slab Lead slab Table 3: Effects of barriers in blocking the β particles. 7

8 Part F: Questions 1. How many protons, how many neutrons and how many electrons does 40 K19 have? Explain. 2. How does the KCl (alone) count-rate compare to the background rate? Answer this question for each observed value of d. 3. From the experiments, which materials were most effective at stopping the β particles? Which material was the least effective? 4. A characteristic time that tells you how unstable is a radioactive nucleus is the half-life, denoted as T1/2. This is the time it takes for half of an original quantity of a radioactive isotope to decay. For example, radium-226 (radium with a total of 226 protons and neutrons) has a half-life of 1,620 years. This means that half of any given specimen of radium-226 will be converted into other elements by the end of 1,620 years. In contrast, 40 K19 has a much longer half-life of 1,260,000,000 years or 1.26x 10 9 years. Suppose you succeed in assembling 1 kilogram of pure 40 K19. How long will it take for you to have a. Half a kilogram b. Quarter a kilogram c. One eighth of a kilogram d. Compute the same for radium 8

9 5. The mean life τ of a radioactive nucleus can be defined by the relation τ = T1/2/ More precisely, τ is the average lifetime of a radioactive nucleus. The number of decays per time of a sample is called the activity A. Activity A = N/ t. Here, N is the number of decays in the time-interval t. It is not difficult to derive the basic result that enables easy computation of the activity: Activity A = N/τ. Here, N is the number of radioactive nuclei in the sample. Use this information to solve the following problem: A typical human adult contains 140 grams of potassium, of which % is the radioactive isotope 40K. This corresponds to about 2.5 x 1020 nuclei of K40. It is the most radioactive part of the human body. From this information, compute the number of disintegrations (i.e., the activity) in one second of 40K in a typical adult. Express your answer in the Standard International unit for activity the Becquerel (Bq). It is defined by 1 Bq = 1 disintegration per second. 9

10 A more traditional unit for activity is the curie (with abbreviation Ci). Its definition is: 1 Ci = 3.70 x disintegrations per second, or 1 Ci = 3.70 x Bq. Express the activity you found in the previous question in terms of Curie. 10